# Argument of a complex number

1. Jan 22, 2017

### cragar

1. The problem statement, all variables and given/known data
Write the given complex number in polar form first using an argument where theta is not equal
to Arg(z)
z=-7i
3. The attempt at a solution
$7isin(\frac{-\pi}{2}+2\pi n)$
The wierd part about this problem it asks me to not use the argument, The argument is the smallest angle of the complex number, So I added 2 pi to it, but it tells me im wrong on my web assign, the only other thing I can think of is taking out the generic n and just adding 2 pi to it.

2. Jan 22, 2017

### haruspex

That's not what I understand by polar form.

3. Jan 22, 2017

### cragar

z=x+iy=rcos(x)+irsin(x), thats not polar form

4. Jan 22, 2017

### haruspex

My mistake, I was thinking of the exponential form.
It's not clear to me which specific variants you tried, like 7i sin(-π/2), 7i sin(3π/2).
As far as I can make out, there is not universal agreement whether Arg is defined to be in the range (-π, π] or [0, 2π).

5. Jan 22, 2017

### cragar

I tried 7isin(-pi/2) ,and the one with a generic 2*pi*n, I might have to wait till my teacher gets back to me on e-mail, because im not sure what my web assign is looking for, I might try 3*pi/2 and then add 2*pi to it, Just wanted to make sure I was interpreting it correctly . thanks for the replies